Shrinking Mount Everest: How to Measure a Mountain
Mount Everest is the second peak from the left.
Credit: Pavel Novak

The magnitude-7.8 earthquake that rocked Nepal on Saturday (April 25) may have caused the world's tallest mountain to shrink a bit. But just how do scientists measure that change?

Official measures put Mount Everest at 29,029 feet (8,848 meters) above sea level, but recent satellite data suggest the sky-scraping peak may have shrunk by about 1 inch (2.54 centimeters), because the underlying tectonic plates have relaxed somewhat.

Accurately measuring miniscule changes in a mountain that is more than 5 miles up is no easy feat, but surprisingly, measurements rely on geometric formulas and surveying techniques that haven't changed all that much since the 1800s, said Peter Molnar, a geologist at the University of Colorado, Boulder. [Photos: The World's Tallest Mountains]

Historic effort

At heart, measuring a mountain relies on basic ninth-grade math. To calculate the elevation of a mountain, scientists would measure the distance between two points on the ground and then measure the angles between the top of the mountain and each point.

"If you have two angles, you know the third, because the sum of the angles is 180 [degrees]," Molnar told Live Science.

To carry out these measurements, surveyors must identify a horizontal surface using a level (which, like the kind at a hardware store, relies on a trapped air bubble that, under the influence of gravity, slides closer to or farther away from a central region as it tilts). From there, surveyors eye the summit and measure the angle with the assistance of a glorified, highly accurate protractor — a telescopic device known as a theodolite. With two angles and one side of a triangle, trigonometry reveals the lengths of the other sides, and thereby, the height of the triangle (the mountain).

Welsh surveyor and geographer Sir George Everest used just this repetitive technique to measure the height of the world's tallest mountain located in the Himalayas in the 1840s. Of course, one measure could be mistaken, so teams of geographers calculated the dimensions of the mountain from myriad different stations at the base of the mountain, averaging out the heights calculated with many, many triangles.

Legend has it that when the team took the average of all of those measurements, they found the mountain was exactly 29,000 feet (8,839 m) tall, Molnar said.

"They didn't expect anybody to believe it, so the story is they added 2 feet [0.6 m], just to make it look more believable," Molnar said.

The official height of Mount Everest is based on a survey conducted in 1955.

Minor adjustments

Nowadays, however, basic trigonometry gets a boost from an army of satellites circling the globe. When a satellite pings a receiver tower on Earth, it can calculate that point's location in a given coordinate system with incredible precision; the calculation relies on two known factors: the radio signal travels at the speed of light; and the satellite is located at a known position relative to the Earth's center at a given time. Because geographers placed a receiver tower near the top of Everest, they were able to get a more precise measure of its height.

In addition, the Earth is curved. That means the distance between two points on the ground is actually an underestimate, and the error is proportional to the distance between the two points divided by the radius of the Earth. That means two surveying stations can't be more than a few miles apart before reasonable amounts of error creep in, Molnar said. [50 Amazing Facts About Earth]

And even that is an approximation. The Earth isn't perfectly spherical; it has a bulge at the equator, making the poles 16 miles (26 km) closer to the center of the Earth than a point on the equator. To account for that discrepancy, surveyors need to add another correction term, Molnar said.

Carrying sea level

Based on tradition, mountains are typically measured not from their bases, but from sea level, which is typically considered the average of the low and high tides in an area.

Unfortunately, "sea level is not level," Molnar said.

The distance from the center of the Earth to the coastline is different around the world, not only because of winds and weather, but also as a result of the Earth's midsection bulge, which causes water (and everything else) to spread out at the equator, Molnar said. In addition, Earth is lumpy, with massive topographical features (such as mountains) altering the gravity in surrounding areas.

"If you measured sea level coming from Calcutta to Nepal, or coming from Bombay, you might wind up with a different answer," Molnar said, referring to the Indian cities that are now called Kolkata and Mumbai, respectively.

The sea level in reference to Everest was first measured during the Great Trigonometric Survey, a Herculean effort to survey the height of the world's tallest mountains, to measure the curvature of the Earth and mean sea level in British India. People "carried in" sea level , bringing the measurement done at the coast inland by marching miles and miles from the coast to Nepal with two bars. They measured the elevation change over a given ground distance by calculating the difference between the height of the two bars using a mounted, swiveling level, according to the Himalayan Club, a climbing and expedition club that provides scholarly information and history on the Himalayas.

Nowadays, geographers use a mathematical expression to estimate sea level. They imagine what would happen if there were no winds or tides, and all the water from the seas could reach interior continental areas by means of tiny, narrow channels. This creates an idealized bumpy, irregularly shaped spheroid that represents mean sea level, called a geoid, from which elevations can then be measured, according to the National Oceanic and Atmospheric Administration.

Despite sophisticated gravimeters, complicated equations and fancy tools like global positioning systems, the elevation of Mount Everest is only precise to within a foot or two.

"All of our elevations have an error," Molnar said.

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